# GaloisGroupUtilities RΒΆ

GaloisGroupUtilities provides several useful functions.

fillPascalTriangle: () -> Void

`fillPascalTriangle()` fills the stored table.

pascalTriangle: (NonNegativeInteger, Integer) -> R

`pascalTriangle(n, r)` returns the binomial coefficient `C(n, r)=n!/(r! (n-r)!)` and stores it in a table to prevent recomputation.

rangePascalTriangle: () -> NonNegativeInteger

`rangePascalTriangle()` returns the maximal number of lines stored.

rangePascalTriangle: NonNegativeInteger -> NonNegativeInteger

`rangePascalTriangle(n)` sets the maximal number of lines which are stored and returns the previous value.

safeCeiling: R -> Integer if R has FloatingPointSystem

`safeCeiling(x)` returns the integer which is greater than any integer with the same floating point number representation.

safeFloor: R -> Integer if R has FloatingPointSystem

`safeFloor(x)` returns the integer which is lower or equal to the largest integer which has the same floating point number representation.

safetyMargin: () -> NonNegativeInteger if R has FloatingPointSystem

`safetyMargin()` returns the number of low weight digits we do not trust in the floating point representation (used by safeCeiling).

safetyMargin: NonNegativeInteger -> NonNegativeInteger if R has FloatingPointSystem

`safetyMargin(n)` sets to `n` the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by safeCeiling).

sizePascalTriangle: () -> NonNegativeInteger

`sizePascalTriangle()` returns the number of entries currently stored in the table.